- Introduction / Martin Grötschel and Volker Mehrmann
- Life sciences / Peter Deuflhard and Christof Schütte
- Mathematics cures virtual patients / Peter Deuflhard, Ralf Kornhuber, Oliver Sander, Anton Schiela and Martin Weiser
- Advanced mathematical modeling ins systems biology / Alexander Bockmayr, Heike Siebert, Susanna Röblitz, Christof Schütte and Peter Deuflhard
- Design of functional molecules / Christof Schütte, Peter Deuflhard, Frank Noé and Marcus Weber
- Networks / Martin Grötschel, Rolf H. Möhring and Martin Skutella
- Mathematics for telecommunications / Frank Aurzada, Andreas Bley, Andreas Eisenblätter, Hans-Florian Geerdes, Mijail Guillemard, Gitta Kutyniok, Friedrich Philipp, Christian Raack, Michael Scheutzow and Axel Werner
- Towards better solutions in logistics with mathematics / Ralf Borndörfer, Rolf H. Möhring and Martin Skutella
- Traveling efficiently with mathematics / Ralf Borndörfer, Olga Heismann, Marika Karbstein, Christian Liebchen, Rolf Möhring, Andris Möller and Werner Römisch
- A jack of all trades? Solving stochastic mixed-integer nonlinear constraint programs / Thomas Arnold, Timo Berthold, Stefan Heinz, Stefan Vigerske, Rene Henrion, Martin Grötschel, Thorsten Koch, Caren Tischendorf and Werner Römisch
- Production / Carsten Carstensen, Michael Hintermüller, Dietmar Hömberg and Fredi Tröltzsch
- Mathematical modeling of multiscale problems / Wolfgang Dreyer and Barbara Wagner
- Nonlinear programming with applications to production processes / Torsten Bosse, Andreas Griewank, René Henrion, Dietmar Hömberg, Chantal Landry, Hernan Leövey and Werner Römisch
- Phase transformation and separation in solids / Dorothee Knees, Ralf Kornhuber, Christiane Kraus, Alexander Mielke and Jürgen Sprekels
- PDE-constrained optimization with industrial applications / Michael Hintermüller, Dietmar Hömberg, Olaf Klein, Jürgen Sprekels and Fredi Tröltzsch
- Electronic and photonic devices / Volker Mehrmann, Alexander Mielke and Frank Schmidt
- Electronics / Caren Tischendorf, Volker Mehrmann and Kersten Schmidt
- Mathematics for optoelectronic devices / Annegret Glitzky, Alexander Mielke, Lutz Recke, Matthias Wolfrum and Serhiy Yanchuk
- Nanophotonics and nonlinear fiber optics / Shalva Amiranashvili, Uwe Bandelow, Mark Blome, Sven Burger, Frank Schmidt, Kersten Schmidt and Lin Zschiedrich
- Finance / Ulrich Horst
- Securitization, optimal control and forward-backward stochastic differential equations / Gregor Heyne and Peter Imkeller
- Affine and beyond affine processes in finance: LIBOR modelling and stochastic volatility / Peter Friz, Martin Keller-Ressel and Antonis Papapantoleon
- Stochastic simulation methods for optimal stopping and control
- towards multilevel approaches / Dirk Becherer and John Schoenmakers
- Visualization / Konrad Polthier, John Sullivan, Günter M. Ziegler and Hans-Christian Hege
- Geometry processing / Konrad Polthier, Alexander Bobenko, Klaus Hildebrandt, Ralf Kornhuber, Christoph von Tycowicz, Harry Yserentant and Günter M. Ziegler
- Image processing / Hans Lamecker, Hans-Christian Hege, Karsten Tabelow and Jörg Polzehl
- Mathematical visualization / John M. Sullivan, Ulrich Pinkall and Konrad Polthier
- Education / Jürg Kramer, Thomas Lange, Brigitte Lutz-Westphal, Sebastian Tappert and Elke Warmuth
- Improving the public image of math
- public relations, press work and school activities / Rudolf Kellermann and Katja Biermann.

Mathematics: intellectual endeavor, production factor, key technology, key to key technologies? Mathematics is all of these! The last three of its facets have been the focus of the research and development in the Berlin-based DFG Research Center MATHEON in the last twelve years. Through these activities MATHEON has become an international trademark for carrying out creative, application-driven research in mathematics and for cooperating with industrial partners in the solution of complex problems in key technologies. Modern key technologies have become highly sophisticated, integrating aspects of engineering, computer, business and other sciences. Flexible mathematical models, as well as fast and accurate methods for numerical simulation and optimization open new possibilities to handle the indicated complexities, to react quickly, and to explore new options. Researchers in mathematical fields such as Optimization, Discrete Mathematics, Numerical Analysis, Scientific Computing, Applied Analysis and Stochastic Analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematics in the solution of the challenging problems in key technologies. This book presents in seven chapters the highlights of the research work carried out in the MATHEON application areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education. The chapters summarize many of the contributions, put them in the context of current mathematical research activities and outline their impact in various key technologies. To make some of the results more easily accessible to the general public, a large number of "showcases" are presented that illustrate a few success stories